NaNbO3 thin films have been grown under anisotropic biaxial strain on several oxide substrates by liquid-delivery spin metalorganic chemical vapor deposition. Compressive lattice strain of different magnitude, induced by the deposition of NaNbO3 films with varying film thickness on NdGaO3 single crystalline substrates, leads to modifications of film orientation and phase symmetry, which are similar to the phase transitions in Pb-containing oxides near the morphotropic phase boundary. Piezoresponse force microscopy measurements exhibit large out-of-plane polarization components, but no distinctive domain structure, while C-V measurements indicate relaxor properties in these films. When tensile strain is provoked by the epitaxial growth on DyScO3, TbScO3, and GdScO3 single crystalline substrates, NaNbO3 films behave rather like a normal ferroelectric. The application of these rare-earth scandate substrates yields well-ordered ferroelectric stripe domains of the type a1/a2 with coherent domain walls aligned along the [001] substrate direction as long as the films are fully strained. With increasing plastic lattice relaxation, initially, a 2D domain pattern with still exclusively in-plane electric polarization, and finally, domains with in-plane and out-of-plane polar components evolve.